The point of this thread is, as I understand it, that - for whatever reason - the Falklands War doesn't take place (which has some interesting personal consequences for me, but that's a digression). It's looking at the consequences that follow on from that. The how and why the War doesn't start isn't that important, it could be that the Thatcher Government sends a couple of frigates and a hunter-killer submarine Down South in Feb 1982, or Uncle Sam says No, or whatever.
With that in mind, and bearing in mind that this is a digression to the thread: At the time, Operation Condor was in full-swing in Argentina, which had the support of the USA. There was a faction within the US Government that, as of April 1982 OTL, was in favour of supporting Argentina over Britain should push come to shove (this faction was most notably represented by Kirkpatrick). The argument deployed was that it really didn't matter a damn what the USA did, Britain would support it as a part of NATO, and Britain didn't need to be kept sweet. By contrast, Argentina was in the forefront of the fight against Communist Bandits In Latin America, poised to invade the USA with, well, God knows what, but that was the case, such as it was. It was, however, a very small part of the US Administration that thought that way, and the bulk favoured Britain.
At the point where the Task Force started trundling in a southerly direction, once the Great British public realised that the Falklands was not close to the Shetlands, the USA made a lot of effort to try and prevent a shooting war, on the basis that it wanted to be friends with both, and didn't want to be in a position of picking sides. It did, however, make it pretty clear to all involved that if it did come to shooting, it would be siding with the British and not the Argentinians.
At the start, Argentina was not in a good place. The economy was in tatters, there was civil unrest against the junta, Operation Condor was causing issues at home and abroad, and there was a new junta in place which calculated that the UK would essentially do nothing in response to an invasion, except complain to the UN, which would ignore things, and a great victory would be secured. The role of the US was essentially unimportant. Once that decision was made, the events took the course they did.